Neurodegeneration is a feature of many debilitating, incurable age-dependent diseases that affect the nervous system and represent a major threat to the health of elderly persons. Because of the ongoing process of aging experienced by modern societies, the increasing prevalence of neurodegenerative diseases is becoming a global public health concern. A major cause of age-related dementia is Alzheimer’s disease (AD). Currently, there are no effective therapies to slow, stop, or reverse the progression of this disease. However, many studies have suggested that modification of lifestyle factors, such as the introduction of an appropriate diet, can delay or prevent the onset of this disorder. Diet is currently considered to be a crucial factor in controlling health and protecting oneself against oxidative stress and chronic inflammation, and thus against chronic degenerative diseases. A large number of bioactive food compounds may influence the pathological mechanisms underlying AD. Among them, phenolic compounds, omega-3 fatty acids, fat-soluble vitamins, isothiocyanates, and carotenoids seem to be promising. They act not only as antioxidant and anti-inflammatory agents, but also as active modulators of the pathological molecular mechanisms that play a role in AD development, including the formation of amyloid plaques and tau tangles, the main hallmarks of AD pathology. In vivo animal model studies as well as clinical and epidemiological research suggest that nutritional intervention has a positive effect on the health of older people and may prevent age-related cognitive decline, especially when the diet contains more than one bioactive nutrient. The Mediterranean diet and in particular its combination with Dietary Approaches to Stop Hypertension, which is called the MIND diet, are nutritional patterns based on many products rich in bioactive compounds that appear to be the most effective in preventing neurodegeneration. The present review gathers evidence that supports the neuroprotective effect of bioactive substances.